Question: Simplify the following expression: $\dfrac{35n^3}{10n^4}$ You can assume $n \neq 0$.
Answer: $ \dfrac{35n^3}{10n^4} = \dfrac{35}{10} \cdot \dfrac{n^3}{n^4} $ To simplify $\frac{35}{10}$ , find the greatest common factor (GCD) of $35$ and $10$ $35 = 5 \cdot 7$ $10 = 2 \cdot 5$ $ \mbox{GCD}(35, 10) = 5 $ $ \dfrac{35}{10} \cdot \dfrac{n^3}{n^4} = \dfrac{5 \cdot 7}{5 \cdot 2} \cdot \dfrac{n^3}{n^4} $ $\phantom{ \dfrac{35}{10} \cdot \dfrac{3}{4}} = \dfrac{7}{2} \cdot \dfrac{n^3}{n^4} $ $ \dfrac{n^3}{n^4} = \dfrac{n \cdot n \cdot n}{n \cdot n \cdot n \cdot n} = \dfrac{1}{n} $ $ \dfrac{7}{2} \cdot \dfrac{1}{n} = \dfrac{7}{2n} $